A141671 Triangle T(n, k) = n/k if n mod k = 0, otherwise T(n, k) = 0, with T(n, 0) = n+1, read by rows.

1, 2, 1, 3, 2, 1, 4, 3, 0, 1, 5, 4, 2, 0, 1, 6, 5, 0, 0, 0, 1, 7, 6, 3, 2, 0, 0, 1, 8, 7, 0, 0, 0, 0, 0, 1, 9, 8, 4, 0, 2, 0, 0, 0, 1, 10, 9, 0, 3, 0, 0, 0, 0, 0, 1, 11, 10, 5, 0, 0, 2, 0, 0, 0, 0, 1, 12, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 13, 12, 6, 4, 3, 0, 2, 0, 0, 0, 0, 0, 1

Offset

0,2

Comments

Apparently this is different from A141672. - N. J. A. Sloane, Sep 13 2008

For n, k >= 1 this triangle is the same as A126988(n, k). - G. C. Greubel, Mar 16 2024

Links

G. C. Greubel, Rows n = 0..100 of the triangle, flattened

Formula

T(n, k) = n/k if n mod k = 0, otherwise T(n, k) = 0, with T(n, 0) = n+1.

Example

Triangle begins as:
   1;
   2,  1;
   3,  2, 1;
   4,  3, 0, 1;
   5,  4, 2, 0, 1;
   6,  5, 0, 0, 0, 1;
   7,  6, 3, 2, 0, 0, 1;
   8,  7, 0, 0, 0, 0, 0, 1;
   9,  8, 4, 0, 2, 0, 0, 0, 1;
  10,  9, 0, 3, 0, 0, 0, 0, 0, 1;
  11, 10, 5, 0, 0, 2, 0, 0, 0, 0, 1;

Mathematica

T[n_, k_]= If[k==0, n+1, If[Mod[n, k]==0, n/k, 0]];
Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten

Prog

(PARI) T(m, n)={if(m, if(n%m, 0, n/m), n+1)};
for(n=0, 10, for(m=0, n, print1(T(m, n)", "))) \\ Charles R Greathouse IV, Oct 11 2009
(Magma)
A141671:= func< n, k | k eq 0 select n+1 else (n mod k) eq 0 select n/k else 0>;
[A141671(n, k): k in [0..n], n in [0..15]]; // G. C. Greubel, Mar 16 2024
(SageMath)
def A141671(n, k):
    if k==0: return n+1
    elif (n%k==0): return n//k
    else: return 0
flatten([[A141671(n, k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, Mar 16 2024

Crossrefs

Cf. A126988, A141672.

Sequence in context: A334441 A278104 A141672 * A309596 A335442 A226247

Adjacent sequences: A141668 A141669 A141670 * A141672 A141673 A141674

Keyword

nonn,easy,tabl

Author

Roger L. Bagula and Gary W. Adamson and Mats Granvik, Sep 06 2008

Extensions

Edited by G. C. Greubel, Mar 16 2024

Status

approved